In a location where the speed of sound is 353 m/s, a 2 000-Hz sound wave impinge

Question

In a location where the speed of sound is 353 m/s, a 2 000-Hz sound wave impinges on two slits 35.0 cm apart. At what angle is the first maximum of sound intensity located? If the sound wave is replaced by 2.00-cm microwaves, what slit separation gives the same angle for the first maximum of microwave intensity? Your response differs from the correct answer by more than 10%. Double check your calculations, cm If the slit separation is 1.00 mu m, what frequency of light gives the same angle to the first maximum of light intensity?

Explanation / Answer

a)

wavelength = 353/2000 = 0.177 m

let the angle is theta

d * sin(theta) = m * wavelength

for m = 1

0.35 * sin(theta) = 1 * 0.177

solving for theta

theta = 30.3 degree

the angle is 30.3 degree

b)

let the angle is theta

d * sin(theta) = m * wavelength

for m = 1

0.35 * sin(theta) = 1 * 0.02

solving for theta

theta = 3.27 degree

the angle is 3.27 degree

c)

d * sin(theta) = m * wavelength

for m = 1

1 *10^-6 * sin(3.27 degree) = 1 * (3 *10^8/f)

solving for f

f = 5.26 *10^15 Hz

the frequency of the light is 5260 THz

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